We study a second order nonlinear system driven by the vector
$p$-Laplacian, with a multivalued nonlinearity and defined on
the positive time semi-axis $\mathbb{R}_+.$ Using degree
theoretic techniques we solve an auxiliary mixed boundary value
problem defined on the finite interval $[0,n]$ and then via a
diagonalization method we produce a solution for the original
infinite time-horizon system.